diff toolboxes/FullBNT-1.0.7/Kalman/sample_lds.m @ 0:e9a9cd732c1e tip

first hg version after svn

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolboxes/FullBNT-1.0.7/Kalman/sample_lds.m	Tue Feb 10 15:05:51 2015 +0000
@@ -0,0 +1,65 @@
+function [x,y] = sample_lds(F, H, Q, R, init_state, T, models, G, u)
+% SAMPLE_LDS Simulate a run of a (switching) stochastic linear dynamical system.
+% [x,y] = switching_lds_draw(F, H, Q, R, init_state, models, G, u)
+% 
+%   x(t+1) = F*x(t) + G*u(t) + w(t),  w ~ N(0, Q),  x(0) = init_state
+%   y(t) =   H*x(t) + v(t),  v ~ N(0, R)
+%
+% Input:
+% F(:,:,i) - the transition matrix for the i'th model
+% H(:,:,i) - the observation matrix for the i'th model
+% Q(:,:,i) - the transition covariance for the i'th model
+% R(:,:,i) - the observation covariance for the i'th model
+% init_state(:,i) - the initial mean for the i'th model
+% T - the num. time steps to run for
+%
+% Optional inputs:
+% models(t) - which model to use at time t. Default = ones(1,T)
+% G(:,:,i) - the input matrix for the i'th model. Default = 0.
+% u(:,t)   - the input vector at time t. Default = zeros(1,T)
+%
+% Output:
+% x(:,t)    - the hidden state vector at time t.
+% y(:,t)    - the observation vector at time t.
+
+
+if ~iscell(F)
+  F = num2cell(F, [1 2]);
+  H = num2cell(H, [1 2]);
+  Q = num2cell(Q, [1 2]);
+  R = num2cell(R, [1 2]);
+end
+
+M = length(F);
+%T = length(models);
+
+if nargin < 7,
+  models = ones(1,T);
+end
+if nargin < 8,
+  G = num2cell(repmat(0, [1 1 M]));
+  u = zeros(1,T);
+end
+
+[os ss] = size(H{1});
+state_noise_samples = cell(1,M);
+obs_noise_samples = cell(1,M);
+for i=1:M
+  state_noise_samples{i} = sample_gaussian(zeros(length(Q{i}),1), Q{i}, T)';
+  obs_noise_samples{i} = sample_gaussian(zeros(length(R{i}),1), R{i}, T)';
+end
+
+x = zeros(ss, T);
+y = zeros(os, T);
+
+m = models(1);
+x(:,1) = init_state(:,m);
+y(:,1) = H{m}*x(:,1) + obs_noise_samples{m}(:,1);
+
+for t=2:T
+  m = models(t);
+  x(:,t) = F{m}*x(:,t-1) + G{m}*u(:,t-1) + state_noise_samples{m}(:,t);
+  y(:,t) = H{m}*x(:,t)  + obs_noise_samples{m}(:,t);
+end
+
+